**Torsional Properties of Fiber:**

It is the property of **textile fibers** or materials when a torsional force is applied on it. The torsional properties determine how fiber respond while being twisted. Here Torsional force is a twisting force that is applied on the two ends of the material in two opposite direction. The behaviors which are shown by a textile material when it is subjected to a torsional force is called torsional property. The shear modulus of a fiber can be determined through torsional testing.

Torsional properties of fiber are..

- Torsional rigidity
- Breaking twist
- Shear modulus

**Above torsional properties of fiber are described below.**

**1. Torsional rigidity: **

Torsional rigidity can be defined as the torque required against twisting is done for which torque is termed as torsional rigidity. The torsional rigidity of a fiber, its resistance to twisting, is defined as the couple needed to put in unit **twist**, that is, unit angular deflection between the ends of a specimen of unit length. Torsional rigidity is very much affected by moisture, fibers being easier to twist as their regain increases.

Mathematically,

——————————————-Torque

Torsional rigidity = ——————————————————–

——————————-Unit twist per unit length

—-ηεc^{2}

= ———–

—–ρ

Where,

ε = Shape factor,

η = Specific shear modulus (N/tex)

c = Linear density

ρ = Density of fiber

From similar considerations, it can be shown that, as fineness varies and other things are equal, resistance to torsion increases more rapidly than fiber linear density. Hence fineness plays a part in determining the ease with which fibers can be twisted together during yarn formation.

The torsional rigidity can be obtained in terms of the shear modulus (or modulus of rigidity) in the same way that the flexural rigidity can be obtained in terms of the tensile modulus, since twisting bears the same relation to shearing as bending does to stretching.

**Specific torsional rigidity:** Specific torsional rigidity can be defined as the torsional rigidity of a fiber of unit linear density.

Mathematically, specific torsional rigidity = ηε/ρ

Unit: N-m^{2}/Tex

**Specific torsional rigidity of different textile fibers:**

Fiber | Specific torsional rigidity (mN-mm^{2}/tex) |

Cotton | 0.16 |

Wool | 0.12 |

Silk | 0.16 |

Viscose | 0.085 |

Nylon-6.6 | 0.06 |

Polyester | 0.067 |

**2. Breaking twist:
**The twist for breaking of a yarn is called breaking twist. It also can be defined as the number of twists required to break a yarn. Breaking twist depends on the diameter of fiber and it is inversely proportional to its diameter. That is, τ

_{b}∞ 1/d

Where,

τ_{b} = Breaking twist,

d = diameter of fiber

**Breaking twist angle (BTA):** This is the angle through which outer layer of fiber are sheared at breaking.

Mathematically, α = tan^{-1}(πdτ_{b})

Where,

α = breaking twist angle,

d = diameter of fiber,

τ_{b} = breaking twist per unit length

**Breaking twist angle of different textile fibers:**

Fiber | Breaking twist angle (α) | Fiber | Breaking twist angle (α) |

Cotton | 35° | Wool | 40° |

Viscose | 33° | Silk | 39° |

Polyester | 50° | Glass | 4° |

**3. Shear modulus: **

The shear modulus is defined as the ratio of shear stress to shear strain, the shear strain being measured in radians. Shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ. Shear modulus’ derived SI unit is the pascal (Pa), although it is usually expressed in gigapascals (GPa) or in thousands of pounds per square inch (ksi). Its dimensional form is M^{1}L^{−1}T^{−2}.

**Torsional Properties of Different Textile Fibers:**

Fiber | Specific flexural rigidity (m N mm2/tex2) | Modulus GPa | Specific torsional rigidity (MIN mm2/tex2) |
Shear modulus (kN/mm2) | |

bending | tension | ||||

Cotton | 0.53 | 7.7 | 0.16 | ||

Viscose rayon | |||||

Fibro (staple) | 0.35 | 10 | 8.7 | 0.058-0.083 | 0.84-1.2 |

Vince! (high wet modulus) | 0.69 | 20 | 0.097 | 1.4 | |

Secondary acetate | 0.25 | 4.2 | 0.064 | ||

Triacetate | 0.25 | 3.8 | 0.091 | ||

Wool | 0.24 | 3.9 | 5.2 | 0.12 | 1.3 |

Silk | 0.60 | 14 | 0.16 | ||

Casein Fibrolane |
0.18 | 2.3 | 0.11 | ||

Nylon 6.6 (3 types) | 0.15-0.22 | 2.5-3.6 | 1.9-3.8 | 0.041-0.060 | 0.033-0.48 |

Polyester fiberTerylene |
0.30 | 7.7 | 6.2 | 0.067 | 0.85 |

Acrylic fiber (3 types) |
0.33-0.48 | 6.0-8.1 | 4.9-7.0 | 0.12-0.18 | 1.0-1.6 |

Polypropylene | 0.51 | 5.2 | 2.4 | 0.14 | 0.75 |

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Founder & Editor of Textile Learner. He is a Textile Consultant, Blogger & Entrepreneur. He is working as a textile consultant in several local and international companies. He is also a contributor of Wikipedia.